1. Field of the Invention
The present invention relates to a coherent sampled time series and more specifically to a parallel architecture implementation of a digital sampled time series for superresolution temporal spectral estimation.
2. Description of Related Art
A uniformly sampled time series consists of discrete digital samples of a signal. The time series information can be represented by a large data vector. The large data vectors are accumulated in large order matrix arrays that are manipulated in order to produce solutions. In the case of a radar doppler detection system, the solution representing a frequency peak due to a moving target can be represented by spectral scan that can be constructed and exhibited on a display screen. In order to produce finer frequency resolution, a longer coherent time aperture with more samples are used. This results in the larger size matrix arrays to be solved. The computation time required to implement superresolution spectrum analysis with an array of x samples is usually proportional to x.sup.3. This means that doubling the number of sensors increases the computation by a factor of eight.
There are a number of techniques which are used to avoid large matrix problems. Unfortunately, most of these approaches compromise the potential frequency resolution of the system. An example would be the division of a large coherent time aperture into non-overlapping smaller coherent time apertures. These subapertures are represented by small matrix arrays, each with sample orders that are small enough to make matrix operations feasible. However, this procedure reduces the Rayleigh resolution to that of the shorter length subapertures corresponding to the smaller matrix arrays. (The Rayleigh frequency resolution is equal to the reciprocal of the coherent integration time of the aperture.)
Another technique involves autoregressive parametric analysis. This involves the reduction of the order of parametric models to levels small enough to suppress instabilities. The arithmetic instabilities which are manifested in spurious peaks are caused by large noise induced fluctuations in the small eigenvalues of the autocorrelation matrices. These methods also significantly degrade resolution.
The problem to be solved is to obtain high, sub-Rayleigh frequency resolution at moderately low SNR scenarios when the sample orders of the coherent time apertures are too large for matrix based superresolution methods to be practicable. Here the number of samples in the coherent time aperture represent both the order of the time series array and also the order of the covariance matrices which are computed from the complex sample data.
There is an extensive prior art associated with multi-rate signal processing architectures as they apply to voice coding (See "A Digital Signal Processing Approach to Interpolation", R. W. Schafer and L. R. Rabiner, Proc. IEEE, Vol. 61, pp. 692-702, June 1973). The generic architecture for the multirate preprocessor of the superresolution systems consists of sequential operations involving the combination of filtering, base band modulation, and decimation which provides a division of the temporal frequency spectrum into spectral subbands. Different architectures which basically accomplish the same end effect correspond to permutations of the order of the signal processing operations.
Superresolution algorithms and their associated architectural embodiments are the class of architectures that produce sub-Rayleigh frequency resolution. Superresolution is often expedited using some form of a matrix approach based upon covariance matrices computed from the elemental complex data for the sampled time series array. Difficulties often occur when the order of the matrices are large, say greater than .about.32. Large matrices are computationally burdensome, and moreover are susceptible to instability problems associated with potential ill-conditioning.
There is a need for an architecture that employs temporal spectral subbanding techniques for the specific purpose of creating effective lower element order pseudo-time series arrays which can be processed in parallel in a matrix based superresolution algorithm/architecture without sacrificing resolution.